LMFDB - Embedded newform 570.2.m.b.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(37,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.7
Root			$-2.20512 + 2.20512i$ of defining polynomial
Character	$\chi$	$=$	570.37
Dual form			570.2.m.b.493.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.114611 - 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.114611 - 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.49802 - 1.66010i) q^{10} -5.29298 q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.91968 + 1.91968i) q^{13} -1.98511 q^{14} +(-1.66010 + 1.49802i) q^{15} -1.00000 q^{16} +(0.488117 + 0.488117i) q^{17} +(0.707107 + 0.707107i) q^{18} +(2.44789 - 3.60663i) q^{19} +(-2.23313 - 0.114611i) q^{20} +1.98511i q^{21} +(-3.74270 + 3.74270i) q^{22} +(-3.88930 + 3.88930i) q^{23} +1.00000i q^{24} +(-4.97373 - 0.511883i) q^{25} +2.71483 q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.40368 + 1.40368i) q^{28} +6.19060 q^{29} +(-0.114611 + 2.23313i) q^{30} -7.84986i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.74270 + 3.74270i) q^{33} +0.690302 q^{34} +(-3.29548 + 2.97373i) q^{35} +1.00000 q^{36} +(-5.60602 + 5.60602i) q^{37} +(-0.819353 - 4.28120i) q^{38} -2.71483i q^{39} +(-1.66010 + 1.49802i) q^{40} +1.90599i q^{41} +(1.40368 + 1.40368i) q^{42} +(7.12884 - 7.12884i) q^{43} +5.29298i q^{44} +(2.23313 + 0.114611i) q^{45} +5.50029i q^{46} +(-7.86994 - 7.86994i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.05934i q^{49} +(-3.87891 + 3.15500i) q^{50} -0.690302i q^{51} +(1.91968 - 1.91968i) q^{52} +(-8.93991 - 8.93991i) q^{53} -1.00000i q^{54} +(-0.606635 + 11.8199i) q^{55} +1.98511i q^{56} +(-4.28120 + 0.819353i) q^{57} +(4.37741 - 4.37741i) q^{58} +0.611185 q^{59} +(1.49802 + 1.66010i) q^{60} +8.31021 q^{61} +(-5.55069 - 5.55069i) q^{62} +(1.40368 - 1.40368i) q^{63} +1.00000i q^{64} +(4.50690 - 4.06687i) q^{65} +5.29298 q^{66} +(-10.2011 + 10.2011i) q^{67} +(0.488117 - 0.488117i) q^{68} +5.50029 q^{69} +(-0.227516 + 4.43300i) q^{70} -3.97022i q^{71} +(0.707107 - 0.707107i) q^{72} +(7.72265 - 7.72265i) q^{73} +7.92810i q^{74} +(3.15500 + 3.87891i) q^{75} +(-3.60663 - 2.44789i) q^{76} +(7.42967 + 7.42967i) q^{77} +(-1.91968 - 1.91968i) q^{78} +17.1528 q^{79} +(-0.114611 + 2.23313i) q^{80} -1.00000 q^{81} +(1.34774 + 1.34774i) q^{82} +(5.43217 - 5.43217i) q^{83} +1.98511 q^{84} +(1.14597 - 1.03408i) q^{85} -10.0817i q^{86} +(-4.37741 - 4.37741i) q^{87} +(3.74270 + 3.74270i) q^{88} -5.42118 q^{89} +(1.66010 - 1.49802i) q^{90} -5.38924i q^{91} +(3.88930 + 3.88930i) q^{92} +(-5.55069 + 5.55069i) q^{93} -11.1298 q^{94} +(-7.77352 - 5.87982i) q^{95} +1.00000 q^{96} +(3.10415 - 3.10415i) q^{97} +(-2.16328 - 2.16328i) q^{98} -5.29298i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	0.114611	−	2.23313i	0.0512557	−	0.998686i
$5$	0.114611	−	2.23313i	0.0512557	−	0.998686i
$6$	−1.00000			−0.408248
$7$	−1.40368	−	1.40368i	−0.530543	−	0.530543i	0.390191	−	0.920734i	$-0.372409\pi$
$7$	−1.40368	−	1.40368i	−0.530543	−	0.530543i	−0.920734	+	0.390191i	$0.872409\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−1.49802	−	1.66010i	−0.473715	−	0.524971i
$11$	−5.29298			−1.59589			−0.797947	−	0.602728i	$-0.794080\pi$
$11$	−5.29298			−1.59589			−0.797947	+	0.602728i	$0.794080\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	1.91968	+	1.91968i	0.532423	+	0.532423i	0.921293	−	0.388870i	$-0.127134\pi$
$13$	1.91968	+	1.91968i	0.532423	+	0.532423i	−0.388870	+	0.921293i	$0.627134\pi$
$14$	−1.98511			−0.530543
$15$	−1.66010	+	1.49802i	−0.428637	+	0.386787i
$16$	−1.00000			−0.250000
$17$	0.488117	+	0.488117i	0.118386	+	0.118386i	0.763818	−	0.645432i	$-0.223323\pi$
$17$	0.488117	+	0.488117i	0.118386	+	0.118386i	−0.645432	+	0.763818i	$0.723323\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	2.44789	−	3.60663i	0.561585	−	0.827419i
$19$	2.44789	−	3.60663i	0.561585	−	0.827419i
$20$	−2.23313	−	0.114611i	−0.499343	−	0.0256278i
$21$			1.98511i			0.433186i
$22$	−3.74270	+	3.74270i	−0.797947	+	0.797947i
$23$	−3.88930	+	3.88930i	−0.810974	+	0.810974i	−0.984780	−	0.173806i	$-0.944393\pi$
$23$	−3.88930	+	3.88930i	−0.810974	+	0.810974i	0.173806	+	0.984780i	$0.444393\pi$
$24$			1.00000i			0.204124i
$25$	−4.97373	−	0.511883i	−0.994746	−	0.102377i
$26$	2.71483			0.532423
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.40368	+	1.40368i	−0.265271	+	0.265271i
$29$	6.19060			1.14956			0.574782	−	0.818306i	$-0.305087\pi$
$29$	6.19060			1.14956			0.574782	+	0.818306i	$0.305087\pi$
$30$	−0.114611	+	2.23313i	−0.0209250	+	0.407712i
$31$		−	7.84986i		−	1.40988i	−0.709268	−	0.704938i	$-0.750975\pi$
$31$		−	7.84986i		−	1.40988i	0.709268	−	0.704938i	$-0.249025\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.74270	+	3.74270i	0.651521	+	0.651521i
$34$	0.690302			0.118386
$35$	−3.29548	+	2.97373i	−0.557039	+	0.502652i
$36$	1.00000			0.166667
$37$	−5.60602	+	5.60602i	−0.921623	+	0.921623i	−0.997144	−	0.0755209i	$-0.975938\pi$
$37$	−5.60602	+	5.60602i	−0.921623	+	0.921623i	0.0755209	+	0.997144i	$0.475938\pi$
$38$	−0.819353	−	4.28120i	−0.132917	−	0.694502i
$39$		−	2.71483i		−	0.434721i
$40$	−1.66010	+	1.49802i	−0.262485	+	0.236857i
$41$			1.90599i			0.297666i	0.988862	+	0.148833i	$0.0475517\pi$
$41$			1.90599i			0.297666i	−0.988862	+	0.148833i	$0.952448\pi$
$42$	1.40368	+	1.40368i	0.216593	+	0.216593i
$43$	7.12884	−	7.12884i	1.08714	−	1.08714i	0.0913152	−	0.995822i	$-0.470893\pi$
$43$	7.12884	−	7.12884i	1.08714	−	1.08714i	0.995822	−	0.0913152i	$-0.0291071\pi$
$44$			5.29298i			0.797947i
$45$	2.23313	+	0.114611i	0.332895	+	0.0170852i
$46$			5.50029i			0.810974i
$47$	−7.86994	−	7.86994i	−1.14795	−	1.14795i	−0.986955	−	0.160993i	$-0.948530\pi$
$47$	−7.86994	−	7.86994i	−1.14795	−	1.14795i	−0.160993	−	0.986955i	$-0.551470\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	3.05934i		−	0.437049i
$50$	−3.87891	+	3.15500i	−0.548561	+	0.446185i
$51$		−	0.690302i		−	0.0966616i
$52$	1.91968	−	1.91968i	0.266211	−	0.266211i
$53$	−8.93991	−	8.93991i	−1.22799	−	1.22799i	−0.964723	−	0.263268i	$-0.915200\pi$
$53$	−8.93991	−	8.93991i	−1.22799	−	1.22799i	−0.263268	−	0.964723i	$-0.584800\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−0.606635	+	11.8199i	−0.0817986	+	1.59380i
$56$			1.98511i			0.265271i
$57$	−4.28120	+	0.819353i	−0.567059	+	0.108526i
$58$	4.37741	−	4.37741i	0.574782	−	0.574782i
$59$	0.611185			0.0795696			0.0397848	−	0.999208i	$-0.487333\pi$
$59$	0.611185			0.0795696			0.0397848	+	0.999208i	$0.487333\pi$
$60$	1.49802	+	1.66010i	0.193393	+	0.214318i
$61$	8.31021			1.06401			0.532007	−	0.846740i	$-0.321438\pi$
$61$	8.31021			1.06401			0.532007	+	0.846740i	$0.321438\pi$
$62$	−5.55069	−	5.55069i	−0.704938	−	0.704938i
$63$	1.40368	−	1.40368i	0.176848	−	0.176848i
$64$			1.00000i			0.125000i
$65$	4.50690	−	4.06687i	0.559013	−	0.504433i
$66$	5.29298			0.651521
$67$	−10.2011	+	10.2011i	−1.24626	+	1.24626i	−0.288905	+	0.957358i	$0.593291\pi$
$67$	−10.2011	+	10.2011i	−1.24626	+	1.24626i	−0.957358	+	0.288905i	$0.906709\pi$
$68$	0.488117	−	0.488117i	0.0591929	−	0.0591929i
$69$	5.50029			0.662158
$70$	−0.227516	+	4.43300i	−0.0271933	+	0.529845i
$71$		−	3.97022i		−	0.471178i	−0.971853	−	0.235589i	$-0.924298\pi$
$71$		−	3.97022i		−	0.471178i	0.971853	−	0.235589i	$-0.0757019\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	7.72265	−	7.72265i	0.903867	−	0.903867i	−0.0919007	−	0.995768i	$-0.529294\pi$
$73$	7.72265	−	7.72265i	0.903867	−	0.903867i	0.995768	+	0.0919007i	$0.0292942\pi$
$74$			7.92810i			0.921623i
$75$	3.15500	+	3.87891i	0.364308	+	0.447898i
$76$	−3.60663	−	2.44789i	−0.413709	−	0.280793i
$77$	7.42967	+	7.42967i	0.846689	+	0.846689i
$78$	−1.91968	−	1.91968i	−0.217361	−	0.217361i
$79$	17.1528			1.92984			0.964918	−	0.262550i	$-0.0845635\pi$
$79$	17.1528			1.92984			0.964918	+	0.262550i	$0.0845635\pi$
$80$	−0.114611	+	2.23313i	−0.0128139	+	0.249671i
$81$	−1.00000			−0.111111
$82$	1.34774	+	1.34774i	0.148833	+	0.148833i
$83$	5.43217	−	5.43217i	0.596258	−	0.596258i	−0.343056	−	0.939315i	$-0.611462\pi$
$83$	5.43217	−	5.43217i	0.596258	−	0.596258i	0.939315	+	0.343056i	$0.111462\pi$
$84$	1.98511			0.216593
$85$	1.14597	−	1.03408i	0.124298	−	0.112162i
$86$		−	10.0817i		−	1.08714i
$87$	−4.37741	−	4.37741i	−0.469308	−	0.469308i
$88$	3.74270	+	3.74270i	0.398973	+	0.398973i
$89$	−5.42118			−0.574644			−0.287322	−	0.957834i	$-0.592765\pi$
$89$	−5.42118			−0.574644			−0.287322	+	0.957834i	$0.592765\pi$
$90$	1.66010	−	1.49802i	0.174990	−	0.157905i
$91$		−	5.38924i		−	0.564946i
$92$	3.88930	+	3.88930i	0.405487	+	0.405487i
$93$	−5.55069	+	5.55069i	−0.575580	+	0.575580i
$94$	−11.1298			−1.14795
$95$	−7.77352	−	5.87982i	−0.797547	−	0.603257i
$96$	1.00000			0.102062
$97$	3.10415	−	3.10415i	0.315178	−	0.315178i	−0.531734	−	0.846912i	$-0.678459\pi$
$97$	3.10415	−	3.10415i	0.315178	−	0.315178i	0.846912	+	0.531734i	$0.178459\pi$
$98$	−2.16328	−	2.16328i	−0.218525	−	0.218525i
$99$		−	5.29298i		−	0.531964i
$100$	−0.511883	+	4.97373i	−0.0511883	+	0.497373i
$101$	−2.79454			−0.278067			−0.139034	−	0.990288i	$-0.544400\pi$
$101$	−2.79454			−0.278067			−0.139034	+	0.990288i	$0.544400\pi$
$102$	−0.488117	−	0.488117i	−0.0483308	−	0.0483308i
$103$	4.05319	+	4.05319i	0.399372	+	0.399372i	0.878012	−	0.478639i	$-0.158870\pi$
$103$	4.05319	+	4.05319i	0.399372	+	0.399372i	−0.478639	+	0.878012i	$0.658870\pi$
$104$		−	2.71483i		−	0.266211i
$105$	4.43300	+	0.227516i	0.432617	+	0.0222033i
$106$	−12.6429			−1.22799
$107$	7.04015	−	7.04015i	0.680597	−	0.680597i	−0.279537	−	0.960135i	$-0.590181\pi$
$107$	7.04015	−	7.04015i	0.680597	−	0.680597i	0.960135	+	0.279537i	$0.0901811\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	8.64011			0.827573			0.413786	−	0.910374i	$-0.364206\pi$
$109$	8.64011			0.827573			0.413786	+	0.910374i	$0.364206\pi$
$110$	7.92898	+	8.78689i	0.755998	+	0.837797i
$111$	7.92810			0.752502
$112$	1.40368	+	1.40368i	0.132636	+	0.132636i
$113$	6.47280	+	6.47280i	0.608910	+	0.608910i	0.942661	−	0.333751i	$-0.108315\pi$
$113$	6.47280	+	6.47280i	0.608910	+	0.608910i	−0.333751	+	0.942661i	$0.608315\pi$
$114$	−2.44789	+	3.60663i	−0.229266	+	0.337792i
$115$	8.23954	+	9.13105i	0.768341	+	0.851475i
$116$		−	6.19060i		−	0.574782i
$117$	−1.91968	+	1.91968i	−0.177474	+	0.177474i
$118$	0.432173	−	0.432173i	0.0397848	−	0.0397848i
$119$		−	1.37032i		−	0.125617i
$120$	2.23313	+	0.114611i	0.203856	+	0.0104625i
$121$	17.0156			1.54688
$122$	5.87621	−	5.87621i	0.532007	−	0.532007i
$123$	1.34774	−	1.34774i	0.121522	−	0.121522i
$124$	−7.84986			−0.704938
$125$	−1.71315	+	11.0483i	−0.153228	+	0.988191i
$126$		−	1.98511i		−	0.176848i
$127$	1.33748	−	1.33748i	0.118683	−	0.118683i	−0.645271	−	0.763954i	$-0.723256\pi$
$127$	1.33748	−	1.33748i	0.118683	−	0.118683i	0.763954	+	0.645271i	$0.223256\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−10.0817			−0.887644
$130$	0.311150	−	6.06257i	0.0272897	−	0.531723i
$131$	5.33670			0.466269			0.233135	−	0.972444i	$-0.425102\pi$
$131$	5.33670			0.466269			0.233135	+	0.972444i	$0.425102\pi$
$132$	3.74270	−	3.74270i	0.325760	−	0.325760i
$133$	−8.49864	+	1.62650i	−0.736926	+	0.141036i
$134$			14.4265i			1.24626i
$135$	−1.49802	−	1.66010i	−0.128929	−	0.142879i
$136$		−	0.690302i		−	0.0591929i
$137$	−2.97373	−	2.97373i	−0.254063	−	0.254063i	0.568571	−	0.822634i	$-0.307496\pi$
$137$	−2.97373	−	2.97373i	−0.254063	−	0.254063i	−0.822634	+	0.568571i	$0.807496\pi$
$138$	3.88930	−	3.88930i	0.331079	−	0.331079i
$139$			13.8993i			1.17892i	0.807796	+	0.589462i	$0.200660\pi$
$139$			13.8993i			1.17892i	−0.807796	+	0.589462i	$0.799340\pi$
$140$	2.97373	+	3.29548i	0.251326	+	0.278519i
$141$			11.1298i			0.937296i
$142$	−2.80737	−	2.80737i	−0.235589	−	0.235589i
$143$	−10.1608	−	10.1608i	−0.849690	−	0.849690i
$144$		−	1.00000i		−	0.0833333i
$145$	0.709511	−	13.8244i	0.0589217	−	1.14805i
$146$		−	10.9215i		−	0.903867i
$147$	−2.16328	+	2.16328i	−0.178425	+	0.178425i
$148$	5.60602	+	5.60602i	0.460812	+	0.460812i
$149$		−	12.9453i		−	1.06052i	−0.847834	−	0.530262i	$-0.822094\pi$
$149$		−	12.9453i		−	1.06052i	0.847834	−	0.530262i	$-0.177906\pi$
$150$	4.97373	+	0.511883i	0.406103	+	0.0417951i
$151$		−	21.7518i		−	1.77013i	−0.465465	−	0.885066i	$-0.654113\pi$
$151$		−	21.7518i		−	1.77013i	0.465465	−	0.885066i	$-0.345887\pi$
$152$	−4.28120	+	0.819353i	−0.347251	+	0.0664583i
$153$	−0.488117	+	0.488117i	−0.0394619	+	0.0394619i
$154$	10.5071			0.846689
$155$	−17.5298	−	0.899682i	−1.40802	−	0.0722642i
$156$	−2.71483			−0.217361
$157$	2.34642	+	2.34642i	0.187264	+	0.187264i	0.794512	−	0.607248i	$-0.207727\pi$
$157$	2.34642	+	2.34642i	0.187264	+	0.187264i	−0.607248	+	0.794512i	$0.707727\pi$
$158$	12.1288	−	12.1288i	0.964918	−	0.964918i
$159$			12.6429i			1.00265i
$160$	1.49802	+	1.66010i	0.118429	+	0.131243i
$161$	10.9187			0.860513
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−14.1411	+	14.1411i	−1.10761	+	1.10761i	−0.114150	+	0.993464i	$0.536414\pi$
$163$	−14.1411	+	14.1411i	−1.10761	+	1.10761i	−0.993464	+	0.114150i	$0.963586\pi$
$164$	1.90599			0.148833
$165$	8.78689	−	7.92898i	0.684058	−	0.617270i
$166$		−	7.68225i		−	0.596258i
$167$	−9.19018	+	9.19018i	−0.711157	+	0.711157i	−0.966777	−	0.255620i	$-0.917720\pi$
$167$	−9.19018	+	9.19018i	−0.711157	+	0.711157i	0.255620	+	0.966777i	$0.417720\pi$
$168$	1.40368	−	1.40368i	0.108297	−	0.108297i
$169$		−	5.62968i		−	0.433052i
$170$	0.0791163	−	1.54153i	0.00606794	−	0.118230i
$171$	3.60663	+	2.44789i	0.275806	+	0.187195i
$172$	−7.12884	−	7.12884i	−0.543569	−	0.543569i
$173$	−2.10806	−	2.10806i	−0.160273	−	0.160273i	0.622415	−	0.782688i	$-0.286152\pi$
$173$	−2.10806	−	2.10806i	−0.160273	−	0.160273i	−0.782688	+	0.622415i	$0.786152\pi$
$174$	−6.19060			−0.469308
$175$	6.26302	+	7.70006i	0.473440	+	0.582070i
$176$	5.29298			0.398973
$177$	−0.432173	−	0.432173i	−0.0324841	−	0.0324841i
$178$	−3.83335	+	3.83335i	−0.287322	+	0.287322i
$179$	7.93836			0.593341			0.296670	−	0.954980i	$-0.404124\pi$
$179$	7.93836			0.593341			0.296670	+	0.954980i	$0.404124\pi$
$180$	0.114611	−	2.23313i	0.00854261	−	0.166448i
$181$			4.77157i			0.354668i	0.984151	+	0.177334i	$0.0567473\pi$
$181$			4.77157i			0.354668i	−0.984151	+	0.177334i	$0.943253\pi$
$182$	−3.81077	−	3.81077i	−0.282473	−	0.282473i
$183$	−5.87621	−	5.87621i	−0.434382	−	0.434382i
$184$	5.50029			0.405487
$185$	11.8764	+	13.1615i	0.873173	+	0.967650i
$186$			7.84986i			0.575580i
$187$	−2.58359	−	2.58359i	−0.188931	−	0.188931i
$188$	−7.86994	+	7.86994i	−0.573974	+	0.573974i
$189$	−1.98511			−0.144395
$190$	−9.65437	+	1.33905i	−0.700402	+	0.0971447i
$191$	−13.8711			−1.00368			−0.501840	−	0.864961i	$-0.667343\pi$
$191$	−13.8711			−1.00368			−0.501840	+	0.864961i	$0.667343\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	8.22061	+	8.22061i	0.591733	+	0.591733i	0.938099	−	0.346367i	$-0.112585\pi$
$193$	8.22061	+	8.22061i	0.591733	+	0.591733i	−0.346367	+	0.938099i	$0.612585\pi$
$194$		−	4.38992i		−	0.315178i
$195$	−6.06257	−	0.311150i	−0.434150	−	0.0222819i
$196$	−3.05934			−0.218525
$197$	−0.844893	−	0.844893i	−0.0601961	−	0.0601961i	0.676368	−	0.736564i	$-0.263553\pi$
$197$	−0.844893	−	0.844893i	−0.0601961	−	0.0601961i	−0.736564	+	0.676368i	$0.763553\pi$
$198$	−3.74270	−	3.74270i	−0.265982	−	0.265982i
$199$		−	17.2265i		−	1.22116i	−0.791956	−	0.610578i	$-0.790937\pi$
$199$		−	17.2265i		−	1.22116i	0.791956	−	0.610578i	$-0.209063\pi$
$200$	3.15500	+	3.87891i	0.223092	+	0.274281i
$201$	14.4265			1.01757
$202$	−1.97604	+	1.97604i	−0.139034	+	0.139034i
$203$	−8.68964	−	8.68964i	−0.609893	−	0.609893i
$204$	−0.690302			−0.0483308
$205$	4.25633	+	0.218448i	0.297275	+	0.0152571i
$206$	5.73207			0.399372
$207$	−3.88930	−	3.88930i	−0.270325	−	0.270325i
$208$	−1.91968	−	1.91968i	−0.133106	−	0.133106i
$209$	−12.9567	+	19.0898i	−0.896230	+	1.32047i
$210$	3.29548	−	2.97373i	0.227410	−	0.205207i
$211$			7.30842i			0.503132i	0.967840	+	0.251566i	$0.0809456\pi$
$211$			7.30842i			0.503132i	−0.967840	+	0.251566i	$0.919054\pi$
$212$	−8.93991	+	8.93991i	−0.613995	+	0.613995i
$213$	−2.80737	+	2.80737i	−0.192358	+	0.192358i
$214$		−	9.95628i		−	0.680597i
$215$	−15.1026	−	16.7367i	−1.02999	−	1.14143i
$216$	−1.00000			−0.0680414
$217$	−11.0187	+	11.0187i	−0.748000	+	0.748000i
$218$	6.10948	−	6.10948i	0.413786	−	0.413786i
$219$	−10.9215			−0.738005
$220$	11.8199	+	0.606635i	0.796898	+	0.0408993i
$221$			1.87405i			0.126063i
$222$	5.60602	−	5.60602i	0.376251	−	0.376251i
$223$	−4.27908	−	4.27908i	−0.286548	−	0.286548i	0.549165	−	0.835714i	$-0.314946\pi$
$223$	−4.27908	−	4.27908i	−0.286548	−	0.286548i	−0.835714	+	0.549165i	$0.814946\pi$
$224$	1.98511			0.132636
$225$	0.511883	−	4.97373i	0.0341255	−	0.331582i
$226$	9.15392			0.608910
$227$	−13.7190	+	13.7190i	−0.910561	+	0.910561i	−0.996316	−	0.0857552i	$-0.972670\pi$
$227$	−13.7190	+	13.7190i	−0.910561	+	0.910561i	0.0857552	+	0.996316i	$0.472670\pi$
$228$	0.819353	+	4.28120i	0.0542630	+	0.283529i
$229$			25.2634i			1.66945i	0.550667	+	0.834725i	$0.314373\pi$
$229$			25.2634i			1.66945i	−0.550667	+	0.834725i	$0.685627\pi$
$230$	12.2829	+	0.630395i	0.809908	+	0.0415670i
$231$		−	10.5071i		−	0.691319i
$232$	−4.37741	−	4.37741i	−0.287391	−	0.287391i
$233$	7.73738	−	7.73738i	0.506892	−	0.506892i	−0.406679	−	0.913571i	$-0.633313\pi$
$233$	7.73738	−	7.73738i	0.506892	−	0.506892i	0.913571	+	0.406679i	$0.133313\pi$
$234$			2.71483i			0.177474i
$235$	−18.4766	+	16.6726i	−1.20528	+	1.08760i
$236$		−	0.611185i		−	0.0397848i
$237$	−12.1288	−	12.1288i	−0.787853	−	0.787853i
$238$	−0.968965	−	0.968965i	−0.0628087	−	0.0628087i
$239$			11.0820i			0.716837i	0.933561	+	0.358418i	$0.116684\pi$
$239$			11.0820i			0.716837i	−0.933561	+	0.358418i	$0.883316\pi$
$240$	1.66010	−	1.49802i	0.107159	−	0.0966967i
$241$			14.5158i			0.935043i	0.883982	+	0.467522i	$0.154853\pi$
$241$			14.5158i			0.935043i	−0.883982	+	0.467522i	$0.845147\pi$
$242$	12.0319	−	12.0319i	0.773438	−	0.773438i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		−	8.31021i		−	0.532007i
$245$	−6.83191	−	0.350635i	−0.436475	−	0.0224013i
$246$		−	1.90599i		−	0.121522i
$247$	11.6227	−	2.22441i	0.739537	−	0.141536i
$248$	−5.55069	+	5.55069i	−0.352469	+	0.352469i
$249$	−7.68225			−0.486843
$250$	6.60096	+	9.02371i	0.417481	+	0.570710i
$251$	6.78199			0.428075			0.214038	−	0.976825i	$-0.431338\pi$
$251$	6.78199			0.428075			0.214038	+	0.976825i	$0.431338\pi$
$252$	−1.40368	−	1.40368i	−0.0884238	−	0.0884238i
$253$	20.5860	−	20.5860i	1.29423	−	1.29423i
$254$		−	1.89149i		−	0.118683i
$255$	−1.54153	−	0.0791163i	−0.0965345	−	0.00495445i
$256$	1.00000			0.0625000
$257$	13.1118	−	13.1118i	0.817891	−	0.817891i	−0.167911	−	0.985802i	$-0.553702\pi$
$257$	13.1118	−	13.1118i	0.817891	−	0.817891i	0.985802	+	0.167911i	$0.0537023\pi$
$258$	−7.12884	+	7.12884i	−0.443822	+	0.443822i
$259$	15.7381			0.977921
$260$	−4.06687	−	4.50690i	−0.252217	−	0.279506i
$261$			6.19060i			0.383188i
$262$	3.77362	−	3.77362i	0.233135	−	0.233135i
$263$	8.10698	−	8.10698i	0.499898	−	0.499898i	−0.411508	−	0.911406i	$-0.634998\pi$
$263$	8.10698	−	8.10698i	0.499898	−	0.499898i	0.911406	+	0.411508i	$0.134998\pi$
$264$		−	5.29298i		−	0.325760i
$265$	−20.9886	+	18.9393i	−1.28932	+	1.16343i
$266$	−4.85934	+	7.15956i	−0.297945	+	0.438981i
$267$	3.83335	+	3.83335i	0.234597	+	0.234597i
$268$	10.2011	+	10.2011i	0.623132	+	0.623132i
$269$	16.5207			1.00729			0.503644	−	0.863911i	$-0.331992\pi$
$269$	16.5207			1.00729			0.503644	+	0.863911i	$0.331992\pi$
$270$	−2.23313	−	0.114611i	−0.135904	−	0.00697501i
$271$	−1.20001			−0.0728953			−0.0364477	−	0.999336i	$-0.511604\pi$
$271$	−1.20001			−0.0728953			−0.0364477	+	0.999336i	$0.511604\pi$
$272$	−0.488117	−	0.488117i	−0.0295964	−	0.0295964i
$273$	−3.81077	+	3.81077i	−0.230638	+	0.230638i
$274$	−4.20549			−0.254063
$275$	26.3258	+	2.70939i	1.58751	+	0.163382i
$276$		−	5.50029i		−	0.331079i
$277$	−5.15378	−	5.15378i	−0.309661	−	0.309661i	0.535117	−	0.844778i	$-0.320268\pi$
$277$	−5.15378	−	5.15378i	−0.309661	−	0.309661i	−0.844778	+	0.535117i	$0.820268\pi$
$278$	9.82829	+	9.82829i	0.589462	+	0.589462i
$279$	7.84986			0.469959
$280$	4.43300	+	0.227516i	0.264923	+	0.0135967i
$281$			21.1406i			1.26114i	0.776132	+	0.630570i	$0.217179\pi$
$281$			21.1406i			1.26114i	−0.776132	+	0.630570i	$0.782821\pi$
$282$	7.86994	+	7.86994i	0.468648	+	0.468648i
$283$	−15.7352	+	15.7352i	−0.935358	+	0.935358i	−0.998034	−	0.0626758i	$-0.980037\pi$
$283$	−15.7352	+	15.7352i	−0.935358	+	0.935358i	0.0626758	+	0.998034i	$0.480037\pi$
$284$	−3.97022			−0.235589
$285$	1.33905	+	9.65437i	0.0793183	+	0.571876i
$286$	−14.3696			−0.849690
$287$	2.67541	−	2.67541i	0.157924	−	0.157924i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	16.5235i		−	0.971970i
$290$	−9.27362	−	10.2770i	−0.544566	−	0.603488i
$291$	−4.38992			−0.257342
$292$	−7.72265	−	7.72265i	−0.451934	−	0.451934i
$293$	11.6988	+	11.6988i	0.683451	+	0.683451i	0.960776	−	0.277325i	$-0.0894478\pi$
$293$	11.6988	+	11.6988i	0.683451	+	0.683451i	−0.277325	+	0.960776i	$0.589448\pi$
$294$			3.05934i			0.178425i
$295$	0.0700487	−	1.36486i	0.00407839	−	0.0794650i
$296$	7.92810			0.460812
$297$	−3.74270	+	3.74270i	−0.217174	+	0.217174i
$298$	−9.15374	−	9.15374i	−0.530262	−	0.530262i
$299$	−14.9324			−0.863562
$300$	3.87891	−	3.15500i	0.223949	−	0.182154i
$301$	−20.0133			−1.15355
$302$	−15.3808	−	15.3808i	−0.885066	−	0.885066i
$303$	1.97604	+	1.97604i	0.113521	+	0.113521i
$304$	−2.44789	+	3.60663i	−0.140396	+	0.206855i
$305$	0.952444	−	18.5578i	0.0545368	−	1.06262i
$306$			0.690302i			0.0394619i
$307$	−13.8361	+	13.8361i	−0.789668	+	0.789668i	−0.981440	−	0.191772i	$-0.938577\pi$
$307$	−13.8361	+	13.8361i	−0.789668	+	0.789668i	0.191772	+	0.981440i	$0.438577\pi$
$308$	7.42967	−	7.42967i	0.423345	−	0.423345i
$309$		−	5.73207i		−	0.326086i
$310$	−13.0316	+	11.7592i	−0.740144	+	0.667880i
$311$	−0.990577			−0.0561705			−0.0280852	−	0.999606i	$-0.508941\pi$
$311$	−0.990577			−0.0561705			−0.0280852	+	0.999606i	$0.508941\pi$
$312$	−1.91968	+	1.91968i	−0.108680	+	0.108680i
$313$	5.68394	−	5.68394i	0.321275	−	0.321275i	−0.527981	−	0.849256i	$-0.677051\pi$
$313$	5.68394	−	5.68394i	0.321275	−	0.321275i	0.849256	+	0.527981i	$0.177051\pi$
$314$	3.31834			0.187264
$315$	−2.97373	−	3.29548i	−0.167551	−	0.185680i
$316$		−	17.1528i		−	0.964918i
$317$	−9.63331	+	9.63331i	−0.541061	+	0.541061i	−0.923840	−	0.382779i	$-0.874967\pi$
$317$	−9.63331	+	9.63331i	−0.541061	+	0.541061i	0.382779	+	0.923840i	$0.374967\pi$
$318$	8.93991	+	8.93991i	0.501325	+	0.501325i
$319$	−32.7667			−1.83458
$320$	2.23313	+	0.114611i	0.124836	+	0.00640696i
$321$	−9.95628			−0.555705
$322$	7.72067	−	7.72067i	0.430256	−	0.430256i
$323$	2.95532	−	0.565601i	0.164438	−	0.0314709i
$324$			1.00000i			0.0555556i
$325$	−8.56530	−	10.5306i	−0.475118	−	0.584133i
$326$			19.9985i			1.10761i
$327$	−6.10948	−	6.10948i	−0.337855	−	0.337855i
$328$	1.34774	−	1.34774i	0.0744165	−	0.0744165i
$329$			22.0938i			1.21807i
$330$	0.606635	−	11.8199i	0.0333941	−	0.650664i
$331$		−	19.9864i		−	1.09855i	−0.835641	−	0.549276i	$-0.814904\pi$
$331$		−	19.9864i		−	1.09855i	0.835641	−	0.549276i	$-0.185096\pi$
$332$	−5.43217	−	5.43217i	−0.298129	−	0.298129i
$333$	−5.60602	−	5.60602i	−0.307208	−	0.307208i
$334$			12.9969i			0.711157i
$335$	21.6112	+	23.9495i	1.18075	+	1.30850i
$336$		−	1.98511i		−	0.108297i
$337$	4.18460	−	4.18460i	0.227950	−	0.227950i	−0.583886	−	0.811836i	$-0.698468\pi$
$337$	4.18460	−	4.18460i	0.227950	−	0.227950i	0.811836	+	0.583886i	$0.198468\pi$
$338$	−3.98078	−	3.98078i	−0.216526	−	0.216526i
$339$		−	9.15392i		−	0.497173i
$340$	−1.03408	−	1.14597i	−0.0560811	−	0.0621490i
$341$			41.5492i			2.25001i
$342$	4.28120	−	0.819353i	0.231501	−	0.0443055i
$343$	−14.1201	+	14.1201i	−0.762416	+	0.762416i
$344$	−10.0817			−0.543569
$345$	0.630395	−	12.2829i	0.0339393	−	0.661287i
$346$	−2.98124			−0.160273
$347$	2.65197	+	2.65197i	0.142365	+	0.142365i	0.774697	−	0.632332i	$-0.217902\pi$
$347$	2.65197	+	2.65197i	0.142365	+	0.142365i	−0.632332	+	0.774697i	$0.717902\pi$
$348$	−4.37741	+	4.37741i	−0.234654	+	0.234654i
$349$		−	17.8125i		−	0.953481i	−0.879044	−	0.476740i	$-0.841818\pi$
$349$		−	17.8125i		−	0.953481i	0.879044	−	0.476740i	$-0.158182\pi$
$350$	9.87339	+	1.01614i	0.527755	+	0.0543151i
$351$	2.71483			0.144907
$352$	3.74270	−	3.74270i	0.199487	−	0.199487i
$353$	−11.6167	+	11.6167i	−0.618293	+	0.618293i	−0.945093	−	0.326801i	$-0.894029\pi$
$353$	−11.6167	+	11.6167i	−0.618293	+	0.618293i	0.326801	+	0.945093i	$0.394029\pi$
$354$	−0.611185			−0.0324841
$355$	−8.86601	−	0.455031i	−0.470559	−	0.0241506i
$356$			5.42118i			0.287322i
$357$	−0.968965	+	0.968965i	−0.0512831	+	0.0512831i
$358$	5.61326	−	5.61326i	0.296670	−	0.296670i
$359$		−	4.76092i		−	0.251272i	−0.992076	−	0.125636i	$-0.959903\pi$
$359$		−	4.76092i		−	0.251272i	0.992076	−	0.125636i	$-0.0400971\pi$
$360$	−1.49802	−	1.66010i	−0.0789525	−	0.0874951i
$361$	−7.01563	−	17.6573i	−0.369243	−	0.929333i
$362$	3.37401	+	3.37401i	0.177334	+	0.177334i
$363$	−12.0319	−	12.0319i	−0.631509	−	0.631509i
$364$	−5.38924			−0.282473
$365$	−16.3606	−	18.1308i	−0.856351	−	0.949008i
$366$	−8.31021			−0.434382
$367$	12.6008	+	12.6008i	0.657754	+	0.657754i	0.954848	−	0.297094i	$-0.0960176\pi$
$367$	12.6008	+	12.6008i	0.657754	+	0.657754i	−0.297094	+	0.954848i	$0.596018\pi$
$368$	3.88930	−	3.88930i	0.202744	−	0.202744i
$369$	−1.90599			−0.0992220
$370$	17.7045	+	0.908649i	0.920412	+	0.0472384i
$371$			25.0976i			1.30300i
$372$	5.55069	+	5.55069i	0.287790	+	0.287790i
$373$	−6.72967	−	6.72967i	−0.348449	−	0.348449i	0.511083	−	0.859532i	$-0.329245\pi$
$373$	−6.72967	−	6.72967i	−0.348449	−	0.348449i	−0.859532	+	0.511083i	$0.829245\pi$
$374$	−3.65375			−0.188931
$375$	9.02371	−	6.60096i	0.465982	−	0.340872i
$376$			11.1298i			0.573974i
$377$	11.8839	+	11.8839i	0.612054	+	0.612054i
$378$	−1.40368	+	1.40368i	−0.0721977	+	0.0721977i
$379$	10.5434			0.541578			0.270789	−	0.962639i	$-0.412715\pi$
$379$	10.5434			0.541578			0.270789	+	0.962639i	$0.412715\pi$
$380$	−5.87982	+	7.77352i	−0.301629	+	0.398773i
$381$	−1.89149			−0.0969039
$382$	−9.80837	+	9.80837i	−0.501840	+	0.501840i
$383$	−8.53662	−	8.53662i	−0.436201	−	0.436201i	0.454530	−	0.890731i	$-0.349807\pi$
$383$	−8.53662	−	8.53662i	−0.436201	−	0.436201i	−0.890731	+	0.454530i	$0.849807\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	17.4429	−	15.7399i	0.888974	−	0.802179i
$386$	11.6257			0.591733
$387$	7.12884	+	7.12884i	0.362379	+	0.362379i
$388$	−3.10415	−	3.10415i	−0.157589	−	0.157589i
$389$		−	25.1180i		−	1.27353i	−0.771056	−	0.636767i	$-0.780271\pi$
$389$		−	25.1180i		−	1.27353i	0.771056	−	0.636767i	$-0.219729\pi$
$390$	−4.50690	+	4.06687i	−0.228216	+	0.205934i
$391$	−3.79686			−0.192016
$392$	−2.16328	+	2.16328i	−0.109262	+	0.109262i
$393$	−3.77362	−	3.77362i	−0.190354	−	0.190354i
$394$	−1.19486			−0.0601961
$395$	1.96590	−	38.3043i	0.0989151	−	1.92730i
$396$	−5.29298			−0.265982
$397$	10.0839	+	10.0839i	0.506098	+	0.506098i	0.913326	−	0.407228i	$-0.133505\pi$
$397$	10.0839	+	10.0839i	0.506098	+	0.506098i	−0.407228	+	0.913326i	$0.633505\pi$
$398$	−12.1810	−	12.1810i	−0.610578	−	0.610578i
$399$	7.15956	+	4.85934i	0.358426	+	0.243271i
$400$	4.97373	+	0.511883i	0.248686	+	0.0255942i
$401$			1.57077i			0.0784407i	0.999231	+	0.0392203i	$0.0124874\pi$
$401$			1.57077i			0.0784407i	−0.999231	+	0.0392203i	$0.987513\pi$
$402$	10.2011	−	10.2011i	0.508785	−	0.508785i
$403$	15.0692	−	15.0692i	0.750651	−	0.750651i
$404$			2.79454i			0.139034i
$405$	−0.114611	+	2.23313i	−0.00569508	+	0.110965i
$406$	−12.2890			−0.609893
$407$	29.6725	−	29.6725i	1.47081	−	1.47081i
$408$	−0.488117	+	0.488117i	−0.0241654	+	0.0241654i
$409$	−10.9037			−0.539153			−0.269576	−	0.962979i	$-0.586884\pi$
$409$	−10.9037			−0.539153			−0.269576	+	0.962979i	$0.586884\pi$
$410$	3.16414	−	2.85521i	0.156266	−	0.141009i
$411$			4.20549i			0.207441i
$412$	4.05319	−	4.05319i	0.199686	−	0.199686i
$413$	−0.857911	−	0.857911i	−0.0422150	−	0.0422150i
$414$	−5.50029			−0.270325
$415$	−11.5082	−	12.7533i	−0.564913	−	0.626036i
$416$	−2.71483			−0.133106
$417$	9.82829	−	9.82829i	0.481293	−	0.481293i
$418$	4.33682	+	22.6603i	0.212121	+	1.10835i
$419$		−	6.93967i		−	0.339025i	−0.985528	−	0.169512i	$-0.945781\pi$
$419$		−	6.93967i		−	0.339025i	0.985528	−	0.169512i	$-0.0542193\pi$
$420$	0.227516	−	4.43300i	0.0111016	−	0.216308i
$421$		−	17.7896i		−	0.867010i	−0.901151	−	0.433505i	$-0.857277\pi$
$421$		−	17.7896i		−	0.867010i	0.901151	−	0.433505i	$-0.142723\pi$
$422$	5.16783	+	5.16783i	0.251566	+	0.251566i
$423$	7.86994	−	7.86994i	0.382650	−	0.382650i
$424$			12.6429i			0.613995i
$425$	−2.17790	−	2.67762i	−0.105644	−	0.129884i
$426$			3.97022i			0.192358i
$427$	−11.6649	−	11.6649i	−0.564505	−	0.564505i
$428$	−7.04015	−	7.04015i	−0.340299	−	0.340299i
$429$			14.3696i			0.693769i
$430$	−22.5137	−	1.15548i	−1.08571	−	0.0557220i
$431$			35.0344i			1.68755i	0.536697	+	0.843775i	$0.319672\pi$
$431$			35.0344i			1.68755i	−0.536697	+	0.843775i	$0.680328\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−14.6222	−	14.6222i	−0.702699	−	0.702699i	0.262290	−	0.964989i	$-0.415522\pi$
$433$	−14.6222	−	14.6222i	−0.702699	−	0.702699i	−0.964989	+	0.262290i	$0.915522\pi$
$434$			15.5828i			0.748000i
$435$	−10.2770	+	9.27362i	−0.492746	+	0.444636i
$436$		−	8.64011i		−	0.413786i
$437$	4.50668	+	23.5479i	0.215584	+	1.12645i
$438$	−7.72265	+	7.72265i	−0.369002	+	0.369002i
$439$	25.2333			1.20432			0.602160	−	0.798376i	$-0.294307\pi$
$439$	25.2333			1.20432			0.602160	+	0.798376i	$0.294307\pi$
$440$	8.78689	−	7.92898i	0.418899	−	0.377999i
$441$	3.05934			0.145683
$442$	1.32516	+	1.32516i	0.0630313	+	0.0630313i
$443$	−17.3294	+	17.3294i	−0.823344	+	0.823344i	−0.986586	−	0.163242i	$-0.947805\pi$
$443$	−17.3294	+	17.3294i	−0.823344	+	0.823344i	0.163242	+	0.986586i	$0.447805\pi$
$444$		−	7.92810i		−	0.376251i
$445$	−0.621328	+	12.1062i	−0.0294538	+	0.573888i
$446$	−6.05153			−0.286548
$447$	−9.15374	+	9.15374i	−0.432957	+	0.432957i
$448$	1.40368	−	1.40368i	0.0663178	−	0.0663178i
$449$	−20.6855			−0.976211			−0.488105	−	0.872785i	$-0.662312\pi$
$449$	−20.6855			−0.976211			−0.488105	+	0.872785i	$0.662312\pi$
$450$	−3.15500	−	3.87891i	−0.148728	−	0.182854i
$451$		−	10.0884i		−	0.475043i
$452$	6.47280	−	6.47280i	0.304455	−	0.304455i
$453$	−15.3808	+	15.3808i	−0.722654	+	0.722654i
$454$			19.4016i			0.910561i
$455$	−12.0349	−	0.617667i	−0.564203	−	0.0289567i
$456$	3.60663	+	2.44789i	0.168896	+	0.114633i
$457$	−7.86170	−	7.86170i	−0.367755	−	0.367755i	0.498903	−	0.866658i	$-0.333736\pi$
$457$	−7.86170	−	7.86170i	−0.367755	−	0.367755i	−0.866658	+	0.498903i	$0.833736\pi$
$458$	17.8639	+	17.8639i	0.834725	+	0.834725i
$459$	0.690302			0.0322205
$460$	9.13105	−	8.23954i	0.425738	−	0.384171i
$461$	23.8664			1.11157			0.555784	−	0.831327i	$-0.312418\pi$
$461$	23.8664			1.11157			0.555784	+	0.831327i	$0.312418\pi$
$462$	−7.42967	−	7.42967i	−0.345659	−	0.345659i
$463$	22.3224	−	22.3224i	1.03741	−	1.03741i	0.0381357	−	0.999273i	$-0.487858\pi$
$463$	22.3224	−	22.3224i	1.03741	−	1.03741i	0.999273	−	0.0381357i	$-0.0121419\pi$
$464$	−6.19060			−0.287391
$465$	11.7592	+	13.0316i	0.545322	+	0.604325i
$466$		−	10.9423i		−	0.506892i
$467$	20.6661	+	20.6661i	0.956312	+	0.956312i	0.999085	−	0.0427727i	$-0.0136191\pi$
$467$	20.6661	+	20.6661i	0.956312	+	0.956312i	−0.0427727	+	0.999085i	$0.513619\pi$
$468$	1.91968	+	1.91968i	0.0887371	+	0.0887371i
$469$	28.6382			1.32239
$470$	−1.27560	+	24.8542i	−0.0588389	+	1.14644i
$471$		−	3.31834i		−	0.152901i
$472$	−0.432173	−	0.432173i	−0.0198924	−	0.0198924i
$473$	−37.7328	+	37.7328i	−1.73495	+	1.73495i
$474$	−17.1528			−0.787853
$475$	−14.0213	+	16.6854i	−0.643343	+	0.765578i
$476$	−1.37032			−0.0628087
$477$	8.93991	−	8.93991i	0.409330	−	0.409330i
$478$	7.83618	+	7.83618i	0.358418	+	0.358418i
$479$		−	15.9212i		−	0.727459i	−0.931505	−	0.363730i	$-0.881503\pi$
$479$		−	15.9212i		−	0.727459i	0.931505	−	0.363730i	$-0.118497\pi$
$480$	0.114611	−	2.23313i	0.00523126	−	0.101928i
$481$	−21.5235			−0.981386
$482$	10.2642	+	10.2642i	0.467522	+	0.467522i
$483$	−7.72067	−	7.72067i	−0.351303	−	0.351303i
$484$		−	17.0156i		−	0.773438i
$485$	−6.57619	−	7.28773i	−0.298609	−	0.330919i
$486$	1.00000			0.0453609
$487$	10.4874	−	10.4874i	0.475228	−	0.475228i	−0.428374	−	0.903602i	$-0.640913\pi$
$487$	10.4874	−	10.4874i	0.475228	−	0.475228i	0.903602	+	0.428374i	$0.140913\pi$
$488$	−5.87621	−	5.87621i	−0.266003	−	0.266003i
$489$	19.9985			0.904363
$490$	−5.07883	+	4.58295i	−0.229438	+	0.207037i
$491$	15.8352			0.714633			0.357317	−	0.933983i	$-0.383692\pi$
$491$	15.8352			0.714633			0.357317	+	0.933983i	$0.383692\pi$
$492$	−1.34774	−	1.34774i	−0.0607608	−	0.0607608i
$493$	3.02173	+	3.02173i	0.136092	+	0.136092i
$494$	6.64563	−	9.79141i	0.299001	−	0.440537i
$495$	−11.8199	−	0.606635i	−0.531265	−	0.0272662i
$496$			7.84986i			0.352469i
$497$	−5.57293	+	5.57293i	−0.249980	+	0.249980i
$498$	−5.43217	+	5.43217i	−0.243422	+	0.243422i
$499$		−	21.1108i		−	0.945050i	−0.881317	−	0.472525i	$-0.843343\pi$
$499$		−	21.1108i		−	0.945050i	0.881317	−	0.472525i	$-0.156657\pi$
$500$	11.0483	+	1.71315i	0.494095	+	0.0766142i
$501$	12.9969			0.580657
$502$	4.79559	−	4.79559i	0.214038	−	0.214038i
$503$	11.3484	−	11.3484i	0.506001	−	0.506001i	−0.407295	−	0.913297i	$-0.633528\pi$
$503$	11.3484	−	11.3484i	0.506001	−	0.506001i	0.913297	+	0.407295i	$0.133528\pi$
$504$	−1.98511			−0.0884238
$505$	−0.320286	+	6.24058i	−0.0142525	+	0.277702i
$506$		−	29.1129i		−	1.29423i
$507$	−3.98078	+	3.98078i	−0.176793	+	0.176793i
$508$	−1.33748	−	1.33748i	−0.0593413	−	0.0593413i
$509$	36.8026			1.63125			0.815624	−	0.578582i	$-0.196394\pi$
$509$	36.8026			1.63125			0.815624	+	0.578582i	$0.196394\pi$
$510$	−1.14597	+	1.03408i	−0.0507445	+	0.0457900i
$511$	−21.6803			−0.959080
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.819353	−	4.28120i	−0.0361753	−	0.189020i
$514$		−	18.5429i		−	0.817891i
$515$	9.51583	−	8.58674i	0.419317	−	0.378377i
$516$			10.0817i			0.443822i
$517$	41.6554	+	41.6554i	1.83200	+	1.83200i
$518$	11.1285	−	11.1285i	0.488960	−	0.488960i
$519$			2.98124i			0.130862i
$520$	−6.06257	−	0.311150i	−0.265861	−	0.0136448i
$521$		−	6.00142i		−	0.262927i	−0.991321	−	0.131463i	$-0.958032\pi$
$521$		−	6.00142i		−	0.262927i	0.991321	−	0.131463i	$-0.0419676\pi$
$522$	4.37741	+	4.37741i	0.191594	+	0.191594i
$523$	19.4311	+	19.4311i	0.849664	+	0.849664i	0.990091	−	0.140427i	$-0.0448476\pi$
$523$	19.4311	+	19.4311i	0.849664	+	0.849664i	−0.140427	+	0.990091i	$0.544848\pi$
$524$		−	5.33670i		−	0.233135i
$525$	1.01614	−	9.87339i	0.0443481	−	0.430910i
$526$		−	11.4650i		−	0.499898i
$527$	3.83165	−	3.83165i	0.166909	−	0.166909i
$528$	−3.74270	−	3.74270i	−0.162880	−	0.162880i
$529$		−	7.25324i		−	0.315358i
$530$	−1.44902	+	28.2333i	−0.0629415	+	1.22638i
$531$			0.611185i			0.0265232i
$532$	1.62650	+	8.49864i	0.0705179	+	0.368463i
$533$	−3.65889	+	3.65889i	−0.158484	+	0.158484i
$534$	5.42118			0.234597
$535$	−14.9147	−	16.5285i	−0.644818	−	0.714587i
$536$	14.4265			0.623132
$537$	−5.61326	−	5.61326i	−0.242230	−	0.242230i
$538$	11.6819	−	11.6819i	0.503644	−	0.503644i
$539$			16.1930i			0.697484i
$540$	−1.66010	+	1.49802i	−0.0714395	+	0.0644644i
$541$	19.3859			0.833467			0.416734	−	0.909029i	$-0.363175\pi$
$541$	19.3859			0.833467			0.416734	+	0.909029i	$0.363175\pi$
$542$	−0.848534	+	0.848534i	−0.0364477	+	0.0364477i
$543$	3.37401	−	3.37401i	0.144793	−	0.144793i
$544$	−0.690302			−0.0295964
$545$	0.990253	−	19.2945i	0.0424178	−	0.826485i
$546$			5.38924i			0.230638i
$547$	−6.28887	+	6.28887i	−0.268893	+	0.268893i	−0.828654	−	0.559761i	$-0.810893\pi$
$547$	−6.28887	+	6.28887i	−0.268893	+	0.268893i	0.559761	+	0.828654i	$0.310893\pi$
$548$	−2.97373	+	2.97373i	−0.127031	+	0.127031i
$549$			8.31021i			0.354671i
$550$	20.5310	−	16.6994i	0.875445	−	0.712063i
$551$	15.1539	−	22.3272i	0.645579	−	0.951171i
$552$	−3.88930	−	3.88930i	−0.165539	−	0.165539i
$553$	−24.0771	−	24.0771i	−1.02386	−	1.02386i
$554$	−7.28855			−0.309661
$555$	0.908649	−	17.7045i	0.0385700	−	0.751513i
$556$	13.8993			0.589462
$557$	9.88148	+	9.88148i	0.418692	+	0.418692i	0.884753	−	0.466061i	$-0.154327\pi$
$557$	9.88148	+	9.88148i	0.418692	+	0.418692i	−0.466061	+	0.884753i	$0.654327\pi$
$558$	5.55069	−	5.55069i	0.234979	−	0.234979i
$559$	27.3701			1.15763
$560$	3.29548	−	2.97373i	0.139260	−	0.125663i
$561$			3.65375i			0.154262i
$562$	14.9486	+	14.9486i	0.630570	+	0.630570i
$563$	16.7009	+	16.7009i	0.703858	+	0.703858i	0.965236	−	0.261379i	$-0.0841771\pi$
$563$	16.7009	+	16.7009i	0.703858	+	0.703858i	−0.261379	+	0.965236i	$0.584177\pi$
$564$	11.1298			0.468648
$565$	15.1965	−	13.7127i	0.639320	−	0.576900i
$566$			22.2529i			0.935358i
$567$	1.40368	+	1.40368i	0.0589492	+	0.0589492i
$568$	−2.80737	+	2.80737i	−0.117795	+	0.117795i
$569$	−1.12910			−0.0473344			−0.0236672	−	0.999720i	$-0.507534\pi$
$569$	−1.12910			−0.0473344			−0.0236672	+	0.999720i	$0.507534\pi$
$570$	7.77352	+	5.87982i	0.325597	+	0.246279i
$571$	−7.89992			−0.330602			−0.165301	−	0.986243i	$-0.552859\pi$
$571$	−7.89992			−0.330602			−0.165301	+	0.986243i	$0.552859\pi$
$572$	−10.1608	+	10.1608i	−0.424845	+	0.424845i
$573$	9.80837	+	9.80837i	0.409750	+	0.409750i
$574$		−	3.78360i		−	0.157924i
$575$	21.3352	−	17.3534i	0.889738	−	0.723688i
$576$	−1.00000			−0.0416667
$577$	−31.1021	−	31.1021i	−1.29480	−	1.29480i	−0.931785	−	0.363011i	$-0.881749\pi$
$577$	−31.1021	−	31.1021i	−1.29480	−	1.29480i	−0.363011	−	0.931785i	$-0.618251\pi$
$578$	−11.6839	−	11.6839i	−0.485985	−	0.485985i
$579$		−	11.6257i		−	0.483148i
$580$	−13.8244	−	0.709511i	−0.574027	−	0.0294609i
$581$	−15.2501			−0.632681
$582$	−3.10415	+	3.10415i	−0.128671	+	0.128671i
$583$	47.3187	+	47.3187i	1.95974	+	1.95974i
$584$	−10.9215			−0.451934
$585$	4.06687	+	4.50690i	0.168144	+	0.186338i
$586$	16.5446			0.683451
$587$	−6.49465	−	6.49465i	−0.268063	−	0.268063i	0.560256	−	0.828319i	$-0.310703\pi$
$587$	−6.49465	−	6.49465i	−0.268063	−	0.268063i	−0.828319	+	0.560256i	$0.810703\pi$
$588$	2.16328	+	2.16328i	0.0892123	+	0.0892123i
$589$	−28.3116	−	19.2156i	−1.16656	−	0.791766i
$590$	−0.915567	−	1.01463i	−0.0376933	−	0.0417717i
$591$			1.19486i			0.0491499i
$592$	5.60602	−	5.60602i	0.230406	−	0.230406i
$593$	16.2871	−	16.2871i	0.668830	−	0.668830i	−0.288615	−	0.957445i	$-0.593195\pi$
$593$	16.2871	−	16.2871i	0.668830	−	0.668830i	0.957445	+	0.288615i	$0.0931948\pi$
$594$			5.29298i			0.217174i
$595$	−3.06011	−	0.157054i	−0.125452	−	0.00643860i
$596$	−12.9453			−0.530262
$597$	−12.1810	+	12.1810i	−0.498535	+	0.498535i
$598$	−10.5588	+	10.5588i	−0.431781	+	0.431781i
$599$	45.2347			1.84824			0.924119	−	0.382104i	$-0.124800\pi$
$599$	45.2347			1.84824			0.924119	+	0.382104i	$0.124800\pi$
$600$	0.511883	−	4.97373i	0.0208975	−	0.203052i
$601$			18.3122i			0.746972i	0.927636	+	0.373486i	$0.121838\pi$
$601$			18.3122i			0.746972i	−0.927636	+	0.373486i	$0.878162\pi$
$602$	−14.1515	+	14.1515i	−0.576773	+	0.576773i
$603$	−10.2011	−	10.2011i	−0.415421	−	0.415421i
$604$	−21.7518			−0.885066
$605$	1.95018	−	37.9981i	0.0792861	−	1.54484i
$606$	2.79454			0.113521
$607$	17.5130	−	17.5130i	0.710829	−	0.710829i	−0.255879	−	0.966709i	$-0.582365\pi$
$607$	17.5130	−	17.5130i	0.710829	−	0.710829i	0.966709	+	0.255879i	$0.0823650\pi$
$608$	0.819353	+	4.28120i	0.0332292	+	0.173626i
$609$			12.2890i			0.497976i
$610$	−12.4489	−	13.7958i	−0.504039	−	0.558576i
$611$		−	30.2155i		−	1.22239i
$612$	0.488117	+	0.488117i	0.0197310	+	0.0197310i
$613$	2.65427	−	2.65427i	0.107205	−	0.107205i	−0.651470	−	0.758675i	$-0.725847\pi$
$613$	2.65427	−	2.65427i	0.107205	−	0.107205i	0.758675	+	0.651470i	$0.225847\pi$
$614$			19.5672i			0.789668i
$615$	−2.85521	−	3.16414i	−0.115133	−	0.127591i
$616$		−	10.5071i		−	0.423345i
$617$	6.67261	+	6.67261i	0.268629	+	0.268629i	0.828548	−	0.559919i	$-0.189168\pi$
$617$	6.67261	+	6.67261i	0.268629	+	0.268629i	−0.559919	+	0.828548i	$0.689168\pi$
$618$	−4.05319	−	4.05319i	−0.163043	−	0.163043i
$619$			21.6368i			0.869657i	0.900513	+	0.434829i	$0.143191\pi$
$619$			21.6368i			0.869657i	−0.900513	+	0.434829i	$0.856809\pi$
$620$	−0.899682	+	17.5298i	−0.0361321	+	0.704012i
$621$			5.50029i			0.220719i
$622$	−0.700444	+	0.700444i	−0.0280852	+	0.0280852i
$623$	7.60962	+	7.60962i	0.304873	+	0.304873i
$624$			2.71483i			0.108680i
$625$	24.4760	+	5.09193i	0.979038	+	0.203677i
$626$		−	8.03830i		−	0.321275i
$627$	22.6603	−	4.33682i	0.904965	−	0.173196i
$628$	2.34642	−	2.34642i	0.0936322	−	0.0936322i
$629$	−5.47278			−0.218214
$630$	−4.43300	−	0.227516i	−0.176615	−	0.00906444i
$631$	−0.652184			−0.0259631			−0.0129815	−	0.999916i	$-0.504132\pi$
$631$	−0.652184			−0.0259631			−0.0129815	+	0.999916i	$0.504132\pi$
$632$	−12.1288	−	12.1288i	−0.482459	−	0.482459i
$633$	5.16783	−	5.16783i	0.205403	−	0.205403i
$634$			13.6236i			0.541061i
$635$	−2.83349	−	3.14007i	−0.112443	−	0.124610i
$636$	12.6429			0.501325
$637$	5.87295	−	5.87295i	0.232695	−	0.232695i
$638$	−23.1696	+	23.1696i	−0.917291	+	0.917291i
$639$	3.97022			0.157059
$640$	1.66010	−	1.49802i	0.0656213	−	0.0592144i
$641$			6.00938i			0.237356i	0.992933	+	0.118678i	$0.0378657\pi$
$641$			6.00938i			0.237356i	−0.992933	+	0.118678i	$0.962134\pi$
$642$	−7.04015	+	7.04015i	−0.277853	+	0.277853i
$643$	−7.37061	+	7.37061i	−0.290669	+	0.290669i	−0.837344	−	0.546676i	$-0.815893\pi$
$643$	−7.37061	+	7.37061i	−0.290669	+	0.290669i	0.546676	+	0.837344i	$0.315893\pi$
$644$		−	10.9187i		−	0.430256i
$645$	−1.15548	+	22.5137i	−0.0454968	+	0.886477i
$646$	1.68979	−	2.48967i	0.0664837	−	0.0979546i
$647$	6.73802	+	6.73802i	0.264899	+	0.264899i	0.827041	−	0.562142i	$-0.190023\pi$
$647$	6.73802	+	6.73802i	0.264899	+	0.264899i	−0.562142	+	0.827041i	$0.690023\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−3.23499			−0.126985
$650$	−13.5028	−	1.38968i	−0.529625	−	0.0545076i
$651$	15.5828			0.610739
$652$	14.1411	+	14.1411i	0.553807	+	0.553807i
$653$	−4.47188	+	4.47188i	−0.174998	+	0.174998i	−0.789171	−	0.614173i	$-0.789490\pi$
$653$	−4.47188	+	4.47188i	−0.174998	+	0.174998i	0.614173	+	0.789171i	$0.289490\pi$
$654$	−8.64011			−0.337855
$655$	0.611645	−	11.9175i	0.0238990	−	0.465657i
$656$		−	1.90599i		−	0.0744165i
$657$	7.72265	+	7.72265i	0.301289	+	0.301289i
$658$	15.6227	+	15.6227i	0.609036	+	0.609036i
$659$	−29.4239			−1.14619			−0.573096	−	0.819489i	$-0.694258\pi$
$659$	−29.4239			−1.14619			−0.573096	+	0.819489i	$0.694258\pi$
$660$	−7.92898	−	8.78689i	−0.308635	−	0.342029i
$661$		−	18.0453i		−	0.701881i	−0.936398	−	0.350941i	$-0.885862\pi$
$661$		−	18.0453i		−	0.701881i	0.936398	−	0.350941i	$-0.114138\pi$
$662$	−14.1325	−	14.1325i	−0.549276	−	0.549276i
$663$	1.32516	−	1.32516i	0.0514648	−	0.0514648i
$664$	−7.68225			−0.298129
$665$	2.65815	+	19.1650i	0.103079	+	0.743186i
$666$	−7.92810			−0.307208
$667$	−24.0771	+	24.0771i	−0.932267	+	0.932267i
$668$	9.19018	+	9.19018i	0.355579	+	0.355579i
$669$			6.05153i			0.233966i
$670$	32.2163	+	1.65344i	1.24462	+	0.0638781i
$671$	−43.9858			−1.69805
$672$	−1.40368	−	1.40368i	−0.0541483	−	0.0541483i
$673$	8.20956	+	8.20956i	0.316455	+	0.316455i	0.847404	−	0.530949i	$-0.178164\pi$
$673$	8.20956	+	8.20956i	0.316455	+	0.316455i	−0.530949	+	0.847404i	$0.678164\pi$
$674$		−	5.91793i		−	0.227950i
$675$	−3.87891	+	3.15500i	−0.149299	+	0.121436i
$676$	−5.62968			−0.216526
$677$	24.0239	−	24.0239i	0.923313	−	0.923313i	−0.0739493	−	0.997262i	$-0.523560\pi$
$677$	24.0239	−	24.0239i	0.923313	−	0.923313i	0.997262	+	0.0739493i	$0.0235603\pi$
$678$	−6.47280	−	6.47280i	−0.248586	−	0.248586i
$679$	−8.71448			−0.334431
$680$	−1.54153	−	0.0791163i	−0.0591151	−	0.00303397i
$681$	19.4016			0.743470
$682$	29.3797	+	29.3797i	1.12501	+	1.12501i
$683$	14.5663	+	14.5663i	0.557363	+	0.557363i	0.928556	−	0.371192i	$-0.121051\pi$
$683$	14.5663	+	14.5663i	0.557363	+	0.557363i	−0.371192	+	0.928556i	$0.621051\pi$
$684$	2.44789	−	3.60663i	0.0935976	−	0.137903i
$685$	−6.98154	+	6.29990i	−0.266751	+	0.240707i
$686$			19.9689i			0.762416i
$687$	17.8639	−	17.8639i	0.681550	−	0.681550i
$688$	−7.12884	+	7.12884i	−0.271784	+	0.271784i
$689$		−	34.3235i		−	1.30762i
$690$	−8.23954	−	9.13105i	−0.313674	−	0.347613i
$691$	−39.3797			−1.49807			−0.749037	−	0.662528i	$-0.769483\pi$
$691$	−39.3797			−1.49807			−0.749037	+	0.662528i	$0.769483\pi$
$692$	−2.10806	+	2.10806i	−0.0801363	+	0.0801363i
$693$	−7.42967	+	7.42967i	−0.282230	+	0.282230i
$694$	3.75046			0.142365
$695$	31.0389	+	1.59302i	1.17737	+	0.0604265i
$696$			6.19060i			0.234654i
$697$	−0.930347	+	0.930347i	−0.0352394	+	0.0352394i
$698$	−12.5953	−	12.5953i	−0.476740	−	0.476740i
$699$	−10.9423			−0.413876
$700$	7.70006	−	6.26302i	0.291035	−	0.236720i
$701$	5.40623			0.204190			0.102095	−	0.994775i	$-0.467445\pi$
$701$	5.40623			0.204190			0.102095	+	0.994775i	$0.467445\pi$
$702$	1.91968	−	1.91968i	0.0724536	−	0.0724536i
$703$	6.49592	+	33.9418i	0.244998	+	1.28014i
$704$		−	5.29298i		−	0.199487i
$705$	24.8542	+	1.27560i	0.936064	+	0.0480418i
$706$			16.4284i			0.618293i
$707$	3.92266	+	3.92266i	0.147527	+	0.147527i
$708$	−0.432173	+	0.432173i	−0.0162421	+	0.0162421i
$709$			10.1007i			0.379340i	0.981848	+	0.189670i	$0.0607418\pi$
$709$			10.1007i			0.379340i	−0.981848	+	0.189670i	$0.939258\pi$
$710$	−6.59097	+	5.94746i	−0.247355	+	0.223204i
$711$			17.1528i			0.643279i
$712$	3.83335	+	3.83335i	0.143661	+	0.143661i
$713$	30.5304	+	30.5304i	1.14337	+	1.14337i
$714$			1.37032i			0.0512831i
$715$	−23.8549	+	21.5259i	−0.892124	+	0.805022i
$716$		−	7.93836i		−	0.296670i
$717$	7.83618	−	7.83618i	0.292647	−	0.292647i
$718$	−3.36648	−	3.36648i	−0.125636	−	0.125636i
$719$		−	41.4079i		−	1.54425i	−0.635469	−	0.772126i	$-0.719193\pi$
$719$		−	41.4079i		−	1.54425i	0.635469	−	0.772126i	$-0.280807\pi$
$720$	−2.23313	−	0.114611i	−0.0832238	−	0.00427131i
$721$		−	11.3788i		−	0.423768i
$722$	−17.4464	−	7.52482i	−0.649288	−	0.280045i
$723$	10.2642	−	10.2642i	0.381730	−	0.381730i
$724$	4.77157			0.177334
$725$	−30.7903	−	3.16886i	−1.14352	−	0.117689i
$726$	−17.0156			−0.631509
$727$	16.2887	+	16.2887i	0.604113	+	0.604113i	0.941401	−	0.337288i	$-0.109510\pi$
$727$	16.2887	+	16.2887i	0.604113	+	0.604113i	−0.337288	+	0.941401i	$0.609510\pi$
$728$	−3.81077	+	3.81077i	−0.141236	+	0.141236i
$729$		−	1.00000i		−	0.0370370i
$730$	−24.3891	−	1.25172i	−0.902679	−	0.0463283i
$731$	6.95941			0.257403
$732$	−5.87621	+	5.87621i	−0.217191	+	0.217191i
$733$	−8.03197	+	8.03197i	−0.296667	+	0.296667i	−0.839707	−	0.543040i	$-0.817273\pi$
$733$	−8.03197	+	8.03197i	−0.296667	+	0.296667i	0.543040	+	0.839707i	$0.317273\pi$
$734$	17.8202			0.657754
$735$	4.58295	+	5.07883i	0.169045	+	0.187335i
$736$		−	5.50029i		−	0.202744i
$737$	53.9942	−	53.9942i	1.98890	−	1.98890i
$738$	−1.34774	+	1.34774i	−0.0496110	+	0.0496110i
$739$			2.95079i			0.108546i	0.998526	+	0.0542732i	$0.0172842\pi$
$739$			2.95079i			0.108546i	−0.998526	+	0.0542732i	$0.982716\pi$
$740$	13.1615	−	11.8764i	0.483825	−	0.436587i
$741$	−9.79141	−	6.64563i	−0.359697	−	0.244133i
$742$	17.7467	+	17.7467i	0.651501	+	0.651501i
$743$	−15.8575	−	15.8575i	−0.581756	−	0.581756i	0.353630	−	0.935386i	$-0.384947\pi$
$743$	−15.8575	−	15.8575i	−0.581756	−	0.581756i	−0.935386	+	0.353630i	$0.884947\pi$
$744$	7.84986			0.287790
$745$	−28.9086	−	1.48368i	−1.05913	−	0.0543579i
$746$	−9.51719			−0.348449
$747$	5.43217	+	5.43217i	0.198753	+	0.198753i
$748$	−2.58359	+	2.58359i	−0.0944655	+	0.0944655i
$749$	−19.7643			−0.722172
$750$	1.71315	−	11.0483i	0.0625552	−	0.403427i
$751$			42.3190i			1.54424i	0.635475	+	0.772121i	$0.280804\pi$
$751$			42.3190i			1.54424i	−0.635475	+	0.772121i	$0.719196\pi$
$752$	7.86994	+	7.86994i	0.286987	+	0.286987i
$753$	−4.79559	−	4.79559i	−0.174761	−	0.174761i
$754$	16.8064			0.612054
$755$	−48.5745	−	2.49299i	−1.76781	−	0.0907294i
$756$			1.98511i			0.0721977i
$757$	6.14572	+	6.14572i	0.223370	+	0.223370i	0.809916	−	0.586546i	$-0.199513\pi$
$757$	6.14572	+	6.14572i	0.223370	+	0.223370i	−0.586546	+	0.809916i	$0.699513\pi$
$758$	7.45532	−	7.45532i	0.270789	−	0.270789i
$759$	−29.1129			−1.05673
$760$	1.33905	+	9.65437i	0.0485724	+	0.350201i
$761$	−32.5422			−1.17966			−0.589828	−	0.807529i	$-0.700804\pi$
$761$	−32.5422			−1.17966			−0.589828	+	0.807529i	$0.700804\pi$
$762$	−1.33748	+	1.33748i	−0.0484520	+	0.0484520i
$763$	−12.1280	−	12.1280i	−0.439063	−	0.439063i
$764$			13.8711i			0.501840i
$765$	1.03408	+	1.14597i	0.0373874	+	0.0414327i
$766$	−12.0726			−0.436201
$767$	1.17328	+	1.17328i	0.0423646	+	0.0423646i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$		−	7.15156i		−	0.257892i	−0.991652	−	0.128946i	$-0.958841\pi$
$769$		−	7.15156i		−	0.257892i	0.991652	−	0.128946i	$-0.0411594\pi$
$770$	1.20424	−	23.4638i	0.0433976	−	0.845576i
$771$	−18.5429			−0.667805
$772$	8.22061	−	8.22061i	0.295866	−	0.295866i
$773$	−28.5163	−	28.5163i	−1.02566	−	1.02566i	−0.999662	−	0.0259998i	$-0.991723\pi$
$773$	−28.5163	−	28.5163i	−1.02566	−	1.02566i	−0.0259998	−	0.999662i	$-0.508277\pi$
$774$	10.0817			0.362379
$775$	−4.01821	+	39.0431i	−0.144338	+	1.40247i
$776$	−4.38992			−0.157589
$777$	−11.1285	−	11.1285i	−0.399234	−	0.399234i
$778$	−17.7611	−	17.7611i	−0.636767	−	0.636767i
$779$	6.87422	+	4.66567i	0.246294	+	0.167165i
$780$	−0.311150	+	6.06257i	−0.0111410	+	0.217075i
$781$			21.0143i			0.751950i
$782$	−2.68479	+	2.68479i	−0.0960078	+	0.0960078i
$783$	4.37741	−	4.37741i	0.156436	−	0.156436i
$784$			3.05934i			0.109262i
$785$	5.50878	−	4.97093i	0.196617	−	0.177420i
$786$	−5.33670			−0.190354
$787$	−38.7817	+	38.7817i	−1.38242	+	1.38242i	−0.542110	+	0.840308i	$0.682374\pi$
$787$	−38.7817	+	38.7817i	−1.38242	+	1.38242i	−0.840308	+	0.542110i	$0.817626\pi$
$788$	−0.844893	+	0.844893i	−0.0300981	+	0.0300981i
$789$	−11.4650			−0.408165
$790$	−25.6952	−	28.4754i	−0.914193	−	1.01311i
$791$		−	18.1715i		−	0.646105i
$792$	−3.74270	+	3.74270i	−0.132991	+	0.132991i
$793$	15.9529	+	15.9529i	0.566505	+	0.566505i
$794$	14.2608			0.506098
$795$	28.2333	+	1.44902i	1.00133	+	0.0513915i
$796$	−17.2265			−0.610578
$797$	2.30137	−	2.30137i	0.0815186	−	0.0815186i	−0.665172	−	0.746690i	$-0.731642\pi$
$797$	2.30137	−	2.30137i	0.0815186	−	0.0815186i	0.746690	+	0.665172i	$0.231642\pi$
$798$	8.49864	−	1.62650i	0.300849	−	0.0575776i
$799$		−	7.68290i		−	0.271802i
$800$	3.87891	−	3.15500i	0.137140	−	0.111546i
$801$		−	5.42118i		−	0.191548i
$802$	1.11070	+	1.11070i	0.0392203	+	0.0392203i
$803$	−40.8758	+	40.8758i	−1.44248	+	1.44248i
$804$		−	14.4265i		−	0.508785i
$805$	1.25140	−	24.3828i	0.0441062	−	0.859381i
$806$		−	21.3111i		−	0.750651i
$807$	−11.6819	−	11.6819i	−0.411223	−	0.411223i
$808$	1.97604	+	1.97604i	0.0695169	+	0.0695169i
$809$		−	14.9375i		−	0.525175i	−0.964908	−	0.262588i	$-0.915424\pi$
$809$		−	14.9375i		−	0.525175i	0.964908	−	0.262588i	$-0.0845759\pi$
$810$	1.49802	+	1.66010i	0.0526350	+	0.0583301i
$811$		−	4.87288i		−	0.171110i	−0.996333	−	0.0855550i	$-0.972734\pi$
$811$		−	4.87288i		−	0.171110i	0.996333	−	0.0855550i	$-0.0272663\pi$
$812$	−8.68964	+	8.68964i	−0.304947	+	0.304947i
$813$	0.848534	+	0.848534i	0.0297594	+	0.0297594i
$814$		−	41.9633i		−	1.47081i
$815$	29.9581	+	33.1995i	1.04939	+	1.16293i
$816$			0.690302i			0.0241654i
$817$	−8.26047	−	43.1617i	−0.288997	−	1.51004i
$818$	−7.71007	+	7.71007i	−0.269576	+	0.269576i
$819$	5.38924			0.188315
$820$	0.218448	−	4.25633i	0.00762854	−	0.148637i
$821$	−56.8328			−1.98348			−0.991739	−	0.128271i	$-0.959057\pi$
$821$	−56.8328			−1.98348			−0.991739	+	0.128271i	$0.959057\pi$
$822$	2.97373	+	2.97373i	0.103721	+	0.103721i
$823$	23.0205	−	23.0205i	0.802444	−	0.802444i	−0.181033	−	0.983477i	$-0.557944\pi$
$823$	23.0205	−	23.0205i	0.802444	−	0.802444i	0.983477	+	0.181033i	$0.0579441\pi$
$824$		−	5.73207i		−	0.199686i
$825$	−16.6994	−	20.5310i	−0.581397	−	0.714798i
$826$	−1.21327			−0.0422150
$827$	−31.6640	+	31.6640i	−1.10106	+	1.10106i	−0.106782	+	0.994282i	$0.534055\pi$
$827$	−31.6640	+	31.6640i	−1.10106	+	1.10106i	−0.994282	+	0.106782i	$0.965945\pi$
$828$	−3.88930	+	3.88930i	−0.135162	+	0.135162i
$829$	−44.3087			−1.53891			−0.769453	−	0.638704i	$-0.779471\pi$
$829$	−44.3087			−1.53891			−0.769453	+	0.638704i	$0.779471\pi$
$830$	−17.1555	−	0.880472i	−0.595475	−	0.0305616i
$831$			7.28855i			0.252837i
$832$	−1.91968	+	1.91968i	−0.0665528	+	0.0665528i
$833$	1.49332	−	1.49332i	0.0517404	−	0.0517404i
$834$		−	13.8993i		−	0.481293i
$835$	19.4695	+	21.5761i	0.673771	+	0.746673i
$836$	19.0898	+	12.9567i	0.660236	+	0.448115i
$837$	−5.55069	−	5.55069i	−0.191860	−	0.191860i
$838$	−4.90709	−	4.90709i	−0.169512	−	0.169512i
$839$	−1.55759			−0.0537739			−0.0268870	−	0.999638i	$-0.508559\pi$
$839$	−1.55759			−0.0537739			−0.0268870	+	0.999638i	$0.508559\pi$
$840$	−2.97373	−	3.29548i	−0.102603	−	0.113705i
$841$	9.32348			0.321499
$842$	−12.5791	−	12.5791i	−0.433505	−	0.433505i
$843$	14.9486	−	14.9486i	0.514858	−	0.514858i
$844$	7.30842			0.251566
$845$	−12.5718	−	0.645224i	−0.432483	−	0.0221964i
$846$		−	11.1298i		−	0.382650i
$847$	−23.8846	−	23.8846i	−0.820683	−	0.820683i
$848$	8.93991	+	8.93991i	0.306998	+	0.306998i
$849$	22.2529			0.763717
$850$	−3.43337	−	0.353354i	−0.117764	−	0.0121199i
$851$		−	43.6069i		−	1.49483i
$852$	2.80737	+	2.80737i	0.0961788	+	0.0961788i
$853$	−8.05684	+	8.05684i	−0.275861	+	0.275861i	−0.831454	−	0.555593i	$-0.812491\pi$
$853$	−8.05684	+	8.05684i	−0.275861	+	0.275861i	0.555593	+	0.831454i	$0.312491\pi$
$854$	−16.4967			−0.564505
$855$	5.87982	−	7.77352i	0.201086	−	0.265849i
$856$	−9.95628			−0.340299
$857$	35.7901	−	35.7901i	1.22257	−	1.22257i	0.255850	−	0.966716i	$-0.417645\pi$
$857$	35.7901	−	35.7901i	1.22257	−	1.22257i	0.966716	−	0.255850i	$-0.0823553\pi$
$858$	10.1608	+	10.1608i	0.346884	+	0.346884i
$859$			49.8517i			1.70092i	0.526042	+	0.850459i	$0.323676\pi$
$859$			49.8517i			1.70092i	−0.526042	+	0.850459i	$0.676324\pi$
$860$	−16.7367	+	15.1026i	−0.570715	+	0.514993i
$861$	−3.78360			−0.128945
$862$	24.7731	+	24.7731i	0.843775	+	0.843775i
$863$	37.1291	+	37.1291i	1.26389	+	1.26389i	0.949192	+	0.314698i	$0.101903\pi$
$863$	37.1291	+	37.1291i	1.26389	+	1.26389i	0.314698	+	0.949192i	$0.398097\pi$
$864$			1.00000i			0.0340207i
$865$	−4.94917	+	4.46596i	−0.168277	+	0.151847i
$866$	−20.6789			−0.702699
$867$	−11.6839	+	11.6839i	−0.396805	+	0.396805i
$868$	11.0187	+	11.0187i	0.374000	+	0.374000i
$869$	−90.7892			−3.07981
$870$	−0.709511	+	13.8244i	−0.0240547	+	0.468691i
$871$	−39.1657			−1.32708
$872$	−6.10948	−	6.10948i	−0.206893	−	0.206893i
$873$	3.10415	+	3.10415i	0.105059	+	0.105059i
$874$	19.8376	+	13.4641i	0.671015	+	0.455431i
$875$	17.9130	−	13.1036i	0.605571	−	0.442983i
$876$			10.9215i			0.369002i
$877$	−9.31345	+	9.31345i	−0.314493	+	0.314493i	−0.846647	−	0.532154i	$-0.821383\pi$
$877$	−9.31345	+	9.31345i	−0.314493	+	0.314493i	0.532154	+	0.846647i	$0.321383\pi$
$878$	17.8426	−	17.8426i	0.602160	−	0.602160i
$879$		−	16.5446i		−	0.558036i
$880$	0.606635	−	11.8199i	0.0204496	−	0.398449i
$881$	−5.39390			−0.181725			−0.0908625	−	0.995863i	$-0.528962\pi$
$881$	−5.39390			−0.181725			−0.0908625	+	0.995863i	$0.528962\pi$
$882$	2.16328	−	2.16328i	0.0728415	−	0.0728415i
$883$	35.2377	−	35.2377i	1.18584	−	1.18584i	0.207637	−	0.978206i	$-0.433423\pi$
$883$	35.2377	−	35.2377i	1.18584	−	1.18584i	0.978206	−	0.207637i	$-0.0665774\pi$
$884$	1.87405			0.0630313
$885$	−1.01463	+	0.915567i	−0.0341064	+	0.0307764i
$886$			24.5074i			0.823344i
$887$	−21.2160	+	21.2160i	−0.712365	+	0.712365i	−0.967029	−	0.254665i	$-0.918035\pi$
$887$	−21.2160	+	21.2160i	−0.712365	+	0.712365i	0.254665	+	0.967029i	$0.418035\pi$
$888$	−5.60602	−	5.60602i	−0.188126	−	0.188126i
$889$	−3.75481			−0.125932
$890$	8.12102	+	8.99971i	0.272217	+	0.301671i
$891$	5.29298			0.177321
$892$	−4.27908	+	4.27908i	−0.143274	+	0.143274i
$893$	−47.6488	+	9.11922i	−1.59451	+	0.305163i
$894$			12.9453i			0.432957i
$895$	0.909824	−	17.7274i	0.0304121	−	0.592561i
$896$		−	1.98511i		−	0.0663178i
$897$	10.5588	+	10.5588i	0.352548	+	0.352548i
$898$	−14.6269	+	14.6269i	−0.488105	+	0.488105i
$899$		−	48.5953i		−	1.62074i
$900$	−4.97373	−	0.511883i	−0.165791	−	0.0170628i
$901$		−	8.72744i		−	0.290753i
$902$	−7.13356	−	7.13356i	−0.237522	−	0.237522i
$903$	14.1515	+	14.1515i	0.470933	+	0.470933i
$904$		−	9.15392i		−	0.304455i
$905$	10.6555	+	0.546876i	0.354202	+	0.0181788i
$906$			21.7518i			0.722654i
$907$	21.1999	−	21.1999i	0.703930	−	0.703930i	−0.261321	−	0.965252i	$-0.584158\pi$
$907$	21.1999	−	21.1999i	0.703930	−	0.703930i	0.965252	+	0.261321i	$0.0841583\pi$
$908$	13.7190	+	13.7190i	0.455281	+	0.455281i
$909$		−	2.79454i		−	0.0926892i
$910$	−8.94669	+	8.07318i	−0.296580	+	0.267623i
$911$		−	45.1425i		−	1.49564i	−0.663903	−	0.747819i	$-0.731101\pi$
$911$		−	45.1425i		−	1.49564i	0.663903	−	0.747819i	$-0.268899\pi$
$912$	4.28120	−	0.819353i	0.141765	−	0.0271315i
$913$	−28.7524	+	28.7524i	−0.951565	+	0.951565i
$914$	−11.1181			−0.367755
$915$	−13.7958	+	12.4489i	−0.456075	+	0.411546i
$916$	25.2634			0.834725
$917$	−7.49104	−	7.49104i	−0.247376	−	0.247376i
$918$	0.488117	−	0.488117i	0.0161103	−	0.0161103i
$919$			12.1007i			0.399165i	0.979881	+	0.199583i	$0.0639586\pi$
$919$			12.1007i			0.399165i	−0.979881	+	0.199583i	$0.936041\pi$
$920$	0.630395	−	12.2829i	0.0207835	−	0.404954i
$921$	19.5672			0.644761
$922$	16.8761	−	16.8761i	0.555784	−	0.555784i
$923$	7.62154	−	7.62154i	0.250866	−	0.250866i
$924$	−10.5071			−0.345659
$925$	30.7524	−	25.0132i	1.01113	−	0.822428i
$926$		−	31.5686i		−	1.03741i
$927$	−4.05319	+	4.05319i	−0.133124	+	0.133124i
$928$	−4.37741	+	4.37741i	−0.143696	+	0.143696i
$929$			22.0342i			0.722920i	0.932388	+	0.361460i	$0.117722\pi$
$929$			22.0342i			0.722920i	−0.932388	+	0.361460i	$0.882278\pi$
$930$	17.5298	+	0.899682i	0.574823	+	0.0295017i
$931$	−11.0339	−	7.48895i	−0.361623	−	0.245440i
$932$	−7.73738	−	7.73738i	−0.253446	−	0.253446i
$933$	0.700444	+	0.700444i	0.0229315	+	0.0229315i
$934$	29.2262			0.956312
$935$	−6.06560	+	5.47339i	−0.198366	+	0.178999i
$936$	2.71483			0.0887371
$937$	−18.3181	−	18.3181i	−0.598425	−	0.598425i	0.341469	−	0.939893i	$-0.389076\pi$
$937$	−18.3181	−	18.3181i	−0.598425	−	0.598425i	−0.939893	+	0.341469i	$0.889076\pi$
$938$	20.2503	−	20.2503i	0.661196	−	0.661196i
$939$	−8.03830			−0.262320
$940$	16.6726	+	18.4766i	0.543801	+	0.602639i
$941$		−	14.4885i		−	0.472310i	−0.971715	−	0.236155i	$-0.924113\pi$
$941$		−	14.4885i		−	0.472310i	0.971715	−	0.236155i	$-0.0758874\pi$
$942$	−2.34642	−	2.34642i	−0.0764504	−	0.0764504i
$943$	−7.41297	−	7.41297i	−0.241399	−	0.241399i
$944$	−0.611185			−0.0198924
$945$	−0.227516	+	4.43300i	−0.00740108	+	0.144206i
$946$			53.3622i			1.73495i
$947$	−9.42564	−	9.42564i	−0.306292	−	0.306292i	0.537177	−	0.843469i	$-0.319491\pi$
$947$	−9.42564	−	9.42564i	−0.306292	−	0.306292i	−0.843469	+	0.537177i	$0.819491\pi$
$948$	−12.1288	+	12.1288i	−0.393926	+	0.393926i
$949$	29.6500			0.962479
$950$	1.88377	+	21.7129i	0.0611175	+	0.704461i
$951$	13.6236			0.441774
$952$	−0.968965	+	0.968965i	−0.0314043	+	0.0314043i
$953$	−24.3168	−	24.3168i	−0.787700	−	0.787700i	0.193417	−	0.981117i	$-0.438043\pi$
$953$	−24.3168	−	24.3168i	−0.787700	−	0.787700i	−0.981117	+	0.193417i	$0.938043\pi$
$954$		−	12.6429i		−	0.409330i
$955$	−1.58979	+	30.9760i	−0.0514443	+	1.00236i
$956$	11.0820			0.358418
$957$	23.1696	+	23.1696i	0.748965	+	0.748965i
$958$	−11.2580	−	11.2580i	−0.363730	−	0.363730i
$959$			8.34835i			0.269582i
$960$	−1.49802	−	1.66010i	−0.0483483	−	0.0535796i
$961$	−30.6203			−0.987753
$962$	−15.2194	+	15.2194i	−0.490693	+	0.490693i
$963$	7.04015	+	7.04015i	0.226866	+	0.226866i
$964$	14.5158			0.467522
$965$	19.2999	−	17.4155i	0.621284	−	0.560625i
$966$	−10.9187			−0.351303
$967$	−2.49180	−	2.49180i	−0.0801310	−	0.0801310i	0.665905	−	0.746036i	$-0.268045\pi$
$967$	−2.49180	−	2.49180i	−0.0801310	−	0.0801310i	−0.746036	+	0.665905i	$0.768045\pi$
$968$	−12.0319	−	12.0319i	−0.386719	−	0.386719i
$969$	−2.48967	−	1.68979i	−0.0799796	−	0.0542837i
$970$	−9.80327	−	0.503134i	−0.314764	−	0.0161547i
$971$			55.4935i			1.78087i	0.455110	+	0.890435i	$0.349600\pi$
$971$			55.4935i			1.78087i	−0.455110	+	0.890435i	$0.650400\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	19.5102	−	19.5102i	0.625469	−	0.625469i
$974$		−	14.8314i		−	0.475228i
$975$	−1.38968	+	13.5028i	−0.0445053	+	0.432437i
$976$	−8.31021			−0.266003
$977$	5.49897	−	5.49897i	0.175928	−	0.175928i	−0.613650	−	0.789578i	$-0.710300\pi$
$977$	5.49897	−	5.49897i	0.175928	−	0.175928i	0.789578	+	0.613650i	$0.210300\pi$
$978$	14.1411	−	14.1411i	0.452181	−	0.452181i
$979$	28.6942			0.917070
$980$	−0.350635	+	6.83191i	−0.0112006	+	0.218237i
$981$			8.64011i			0.275858i
$982$	11.1972	−	11.1972i	0.357317	−	0.357317i
$983$	21.9026	+	21.9026i	0.698585	+	0.698585i	0.964105	−	0.265520i	$-0.0855437\pi$
$983$	21.9026	+	21.9026i	0.698585	+	0.698585i	−0.265520	+	0.964105i	$0.585544\pi$
$984$	−1.90599			−0.0607608
$985$	−1.98359	+	1.78992i	−0.0632024	+	0.0570316i
$986$	4.27338			0.136092
$987$	15.6227	−	15.6227i	0.497276	−	0.497276i
$988$	−2.22441	−	11.6227i	−0.0707678	−	0.369769i
$989$			55.4523i			1.76328i
$990$	−8.78689	+	7.92898i	−0.279266	+	0.251999i
$991$		−	37.4884i		−	1.19086i	−0.803408	−	0.595429i	$-0.796982\pi$
$991$		−	37.4884i		−	1.19086i	0.803408	−	0.595429i	$-0.203018\pi$
$992$	5.55069	+	5.55069i	0.176235	+	0.176235i
$993$	−14.1325	+	14.1325i	−0.448482	+	0.448482i
$994$			7.88131i			0.249980i
$995$	−38.4691	−	1.97435i	−1.21955	−	0.0625912i
$996$			7.68225i			0.243422i
$997$	−39.6736	−	39.6736i	−1.25648	−	1.25648i	−0.952763	−	0.303714i	$-0.901773\pi$
$997$	−39.6736	−	39.6736i	−1.25648	−	1.25648i	−0.303714	−	0.952763i	$-0.598227\pi$
$998$	−14.9276	−	14.9276i	−0.472525	−	0.472525i
$999$			7.92810i			0.250834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.b.37.7	yes	20
3.2	odd	2		1710.2.p.c.37.4		20
5.3	odd	4	inner	570.2.m.b.493.2	yes	20
15.8	even	4		1710.2.p.c.1063.9		20
19.18	odd	2	inner	570.2.m.b.37.2	✓	20
57.56	even	2		1710.2.p.c.37.9		20
95.18	even	4	inner	570.2.m.b.493.7	yes	20
285.113	odd	4		1710.2.p.c.1063.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.2	✓	20	19.18	odd	2	inner
570.2.m.b.37.7	yes	20	1.1	even	1	trivial
570.2.m.b.493.2	yes	20	5.3	odd	4	inner
570.2.m.b.493.7	yes	20	95.18	even	4	inner
1710.2.p.c.37.4		20	3.2	odd	2
1710.2.p.c.37.9		20	57.56	even	2
1710.2.p.c.1063.4		20	285.113	odd	4
1710.2.p.c.1063.9		20	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.114611 - 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.114611 - 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.49802 - 1.66010i) q^{10} -5.29298 q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.91968 + 1.91968i) q^{13} -1.98511 q^{14} +(-1.66010 + 1.49802i) q^{15} -1.00000 q^{16} +(0.488117 + 0.488117i) q^{17} +(0.707107 + 0.707107i) q^{18} +(2.44789 - 3.60663i) q^{19} +(-2.23313 - 0.114611i) q^{20} +1.98511i q^{21} +(-3.74270 + 3.74270i) q^{22} +(-3.88930 + 3.88930i) q^{23} +1.00000i q^{24} +(-4.97373 - 0.511883i) q^{25} +2.71483 q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.40368 + 1.40368i) q^{28} +6.19060 q^{29} +(-0.114611 + 2.23313i) q^{30} -7.84986i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.74270 + 3.74270i) q^{33} +0.690302 q^{34} +(-3.29548 + 2.97373i) q^{35} +1.00000 q^{36} +(-5.60602 + 5.60602i) q^{37} +(-0.819353 - 4.28120i) q^{38} -2.71483i q^{39} +(-1.66010 + 1.49802i) q^{40} +1.90599i q^{41} +(1.40368 + 1.40368i) q^{42} +(7.12884 - 7.12884i) q^{43} +5.29298i q^{44} +(2.23313 + 0.114611i) q^{45} +5.50029i q^{46} +(-7.86994 - 7.86994i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.05934i q^{49} +(-3.87891 + 3.15500i) q^{50} -0.690302i q^{51} +(1.91968 - 1.91968i) q^{52} +(-8.93991 - 8.93991i) q^{53} -1.00000i q^{54} +(-0.606635 + 11.8199i) q^{55} +1.98511i q^{56} +(-4.28120 + 0.819353i) q^{57} +(4.37741 - 4.37741i) q^{58} +0.611185 q^{59} +(1.49802 + 1.66010i) q^{60} +8.31021 q^{61} +(-5.55069 - 5.55069i) q^{62} +(1.40368 - 1.40368i) q^{63} +1.00000i q^{64} +(4.50690 - 4.06687i) q^{65} +5.29298 q^{66} +(-10.2011 + 10.2011i) q^{67} +(0.488117 - 0.488117i) q^{68} +5.50029 q^{69} +(-0.227516 + 4.43300i) q^{70} -3.97022i q^{71} +(0.707107 - 0.707107i) q^{72} +(7.72265 - 7.72265i) q^{73} +7.92810i q^{74} +(3.15500 + 3.87891i) q^{75} +(-3.60663 - 2.44789i) q^{76} +(7.42967 + 7.42967i) q^{77} +(-1.91968 - 1.91968i) q^{78} +17.1528 q^{79} +(-0.114611 + 2.23313i) q^{80} -1.00000 q^{81} +(1.34774 + 1.34774i) q^{82} +(5.43217 - 5.43217i) q^{83} +1.98511 q^{84} +(1.14597 - 1.03408i) q^{85} -10.0817i q^{86} +(-4.37741 - 4.37741i) q^{87} +(3.74270 + 3.74270i) q^{88} -5.42118 q^{89} +(1.66010 - 1.49802i) q^{90} -5.38924i q^{91} +(3.88930 + 3.88930i) q^{92} +(-5.55069 + 5.55069i) q^{93} -11.1298 q^{94} +(-7.77352 - 5.87982i) q^{95} +1.00000 q^{96} +(3.10415 - 3.10415i) q^{97} +(-2.16328 - 2.16328i) q^{98} -5.29298i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

Introduction

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